Chapter 25, Problem 22PS

(a)

Interpretation Introduction

Interpretation:

Symbol, atomic number and mass for the unknown particle of the given nuclear reaction have to be identified.

Concept Introduction:

Balancing nuclear reaction equation: The balanced nuclear reaction should conserve both mass number and atomic number.

• The sum of the mass numbers of the reactants should be equal to the sum of mass numbers of the products in the reaction.
• The sum of atomic numbers (or the atomic charge) of the reactants should be equal to the sum of atomic numbers (or the atomic charge) of the products in the reaction.

Explanation of Solution

The bombardment of unknown particle with Beryllium-9, produce an Helium nuclei particle andLithium-6. The unknown particle is predicted by the rule that says the atomic and mass number must be equal.

$\begin{array}{l}Be+X\to Li+He\\ \underset{\_}{CalculateMassNumberA:}\\ 9\left(Be\right)+A\left(X\right)=6\left(Li\right)+4\left(He\right)\\ A=10-9\\ A=1\\ \underset{\_}{CalculateAtomicNumberZ:}\\ 4\left(Be\right)+Z\left(X\right)=3\left(Li\right)+2\left(He\right)\\ Z=5-4\\ Z=1\end{array}$

The elemental representation is, $X$. The atomic number of 1 and the mass number of 1 is a Proton nuclei.

The complete nuclear reaction is $Be+H\to Li+He$.

(b)

Interpretation Introduction

Interpretation:

Symbol, atomic number and mass for the unknown particle of the given nuclear reaction have to be identified.

Concept Introduction:

Balancing nuclear reaction equation: The balanced nuclear reaction should conserve both mass number and atomic number.

• The sum of the mass numbers of the reactants should be equal to the sum of mass numbers of the products in the reaction.
• The sum of atomic numbers (or the atomic charge) of the reactants should be equal to the sum of atomic numbers (or the atomic charge) of the products in the reaction.

Explanation of Solution

The bombardment of neutron particle with unknown nuclei, produce a Sodium-24 and Helium nuclei particle. The unknown particle is predicted by the rule that says the atomic and mass number must be equal.

$\begin{array}{l}X+n\to Na+He\\ \underset{\_}{CalculateMassNumberA:}\\ A\left(X\right)+1\left(neutron\right)=24\left(Na\right)+4\left(He\right)\\ A=28-1\\ A=27\\ \underset{\_}{CalculateAtomicNumberZ:}\\ Z\left(X\right)+0\left(neutron\right)=11\left(Na\right)+2\left(He\right)\\ Z=13-0\\ Z=13\end{array}$

The elemental representation is, $X$. The atomic number of 13 and the mass number of 27 is Aluminum.

The complete nuclear reaction is $Al+n\to Na+He$.

(c)

Interpretation Introduction

Interpretation:

Symbol, atomic number and mass for the unknown particle of the given nuclear reaction have to be identified.

Concept Introduction:

Balancing nuclear reaction equation: The balanced nuclear reaction should conserve both mass number and atomic number.

• The sum of the mass numbers of the reactants should be equal to the sum of mass numbers of the products in the reaction.
• The sum of atomic numbers (or the atomic charge) of the reactants should be equal to the sum of atomic numbers (or the atomic charge) of the products in the reaction.

Explanation of Solution

The bombardment of unknown particle with Calcium-40, produce Proton nuclei particle and Potassium-40. The unknown particle is predicted by the rule that says the atomic and mass number must be equal.

$\begin{array}{l}Ca+X\to K+H\\ \underset{\_}{CalculateMassNumberA:}\\ 40\left(Ca\right)+A\left(X\right)=40\left(K\right)+1\left(H\right)\\ A=41-40\\ A=1\\ \underset{\_}{CalculateAtomicNumberZ:}\\ 20\left(Ca\right)+Z\left(X\right)=19\left(K\right)+1\left(H\right)\\ Z=20-20\\ Z=0\end{array}$

The elemental representation is, $X$. The atomic number of 0 and the mass number of 1 is a Neutron particle.

The complete nuclear reaction is $Ca+n\to K+H$.

(d)

Interpretation Introduction

Interpretation:

Symbol, atomic number and mass for the unknown particle of the given nuclear reaction have to be identified.

Concept Introduction:

Balancing nuclear reaction equation: The balanced nuclear reaction should conserve both mass number and atomic number.

• The sum of the mass numbers of the reactants should be equal to the sum of mass numbers of the products in the reaction.
• The sum of atomic numbers (or the atomic charge) of the reactants should be equal to the sum of atomic numbers (or the atomic charge) of the products in the reaction.

Explanation of Solution

The bombardment of alpha particle with Amercium-241, produce an unknown nuclei particle and Berkelium-243. The unknown particle is predicted by the rule that says the atomic and mass number must be equal.

$\begin{array}{l}Am+He\to Bk+X\\ \underset{\_}{CalculateMassNumberA:}\\ 241\left(Am\right)+4\left(He\right)=243\left(Bk\right)+A\left(X\right)\\ A=245-243\\ A=2\\ \underset{\_}{CalculateAtomicNumberZ:}\\ 95\left(Am\right)+2\left(He\right)=97\left(Bk\right)+Z\left(X\right)\\ Z=97-97\\ Z=0\end{array}$

The elemental representation is, $X$. The atomic number of 0 and the mass number of 2 is two Proton nuclei.

The complete nuclear reaction is $Am+He\to Bk+2n$.

(e)

Interpretation Introduction

Interpretation:

Symbol, atomic number and mass for the unknown particle of the given nuclear reaction have to be identified.

Concept Introduction:

Balancing nuclear reaction equation: The balanced nuclear reaction should conserve both mass number and atomic number.

• The sum of the mass numbers of the reactants should be equal to the sum of mass numbers of the products in the reaction.
• The sum of atomic numbers (or the atomic charge) of the reactants should be equal to the sum of atomic numbers (or the atomic charge) of the products in the reaction.

Explanation of Solution

The bombardment of Carbon-6 particle with Curium-246, produce four neutron particle and an unknown particle. The unknown particle is predicted by the rule that says the atomic and mass number must be equal.

$\begin{array}{l}Cm+C\to 4n+X\\ \underset{\_}{CalculateMassNumberA:}\\ 246\left(Cm\right)+12\left(C\right)=4\left(n\right)+A\left(X\right)\\ A=258-4\\ A=254\\ \underset{\_}{CalculateAtomicNumberZ:}\\ 96\left(Cm\right)+6\left(C\right)=0\left(n\right)+Z\left(X\right)\\ Z=102\end{array}$

The elemental representation is, $X$. The atomic number of 102 and the mass number of 259 is Nobelium isotope.

The complete nuclear reaction is $Cm+C\to 4n+No$.

(f)

Interpretation Introduction

Interpretation:

Symbol, atomic number and mass for the unknown particle of the given nuclear reaction have to be identified.

Concept Introduction:

Balancing nuclear reaction equation: The balanced nuclear reaction should conserve both mass number and atomic number.

• The sum of the mass numbers of the reactants should be equal to the sum of mass numbers of the products in the reaction.
• The sum of atomic numbers (or the atomic charge) of the reactants should be equal to the sum of atomic numbers (or the atomic charge) of the products in the reaction.

Explanation of Solution

The bombardment of unknown particle with Uranium-238, produce five neutron particles and Fermium-249. The unknown particle is predicted by the rule that says the atomic and mass number must be equal.

$\begin{array}{l}U+X\to Fm+5n\\ \underset{\_}{CalculateMassNumberA:}\\ 238\left(U\right)+A\left(X\right)=249\left(Fm\right)+5\left(n\right)\\ A=254-238\\ A=16\\ \underset{\_}{CalculateAtomicNumberZ:}\\ 92\left(U\right)+Z\left(X\right)=100\left(Fm\right)+0\left(n\right)\\ Z=100-92\\ Z=8\end{array}$

The elemental representation is, $X$. The atomic number of 8 and the mass number of 16 is Oxygen isotope.

The complete nuclear reaction is $U+O\to Fm+5n$.